The most widely used free alternative (by many local authorities, for example) is OpenOffice:
http://www.openoffice.org/
LibreOffice is an updated version of the Lotus commercial software that used to be Microsoft Office's biggest rival. (When Lotus ceased to develop it they placed the source code into the public domain):
http://www.libreoffice.org/
KingSoft Office is a relative newcomer but is gaining plenty of fans:
http://www.libreoffice.org/
All of the above are full office
suites, including presentation and database software as well as word processors.
If you ONLY want a word processor, Abiword is very popular:
http://www.abisource.com/